Method and apparatus for phase-matched optical and RF wave propagations for semiconductor based MZM modulators

ABSTRACT

Optical modulators with semiconductor based optical waveguides interacting with an RF waveguide in a traveling wave structure. The semiconductor optical waveguide generally comprise a p-n junction along the waveguide. To reduce the phase walk-off between the optical signal and the RF signal, the traveling wave structure can comprise one or more compensation sections where the phase walk-off is reversed. The compensation sections can comprise a change in dopant concentrations, extra length for the optical waveguide and/or extra length for the RF waveguide. Corresponding methods are described.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of copending U.S. patent applicationSer. No. 15/873,363 filed Jan. 17, 2018 to Jianying Zhou entitled“Method And Apparatus For Phase-Matched Optical And Rf Wave PropagationsFor Semiconductor-Based Mzm Modulators,” which claims priority to U.S.provisional patent application 62/447,521 to Jianying Zhou filed on Jan.18, 2017, entitled “Method and Apparatus for Phase-Matched Optical andRF Wave Propagations for High Speed High Efficiency Linear MZMModulators,” incorporated herein by reference.

FIELD OF THE INVENTION

The invention relates to optical modulators comprising a semiconductoroptical waveguide interfaced with RF waveguides in which electro-opticalcoupling provides a modulation to the optical signal. The inventionfurther relates to waveguide designs to decrease phase shifts betweenpropagating electrical signals and optical intensity propagating throughthe respective waveguides.

BACKGROUND OF THE INVENTION

A traveling wave structure is widely used in high speed linearmodulators with Mach-Zehnder modulator (MZM) structures with traditionalmaterial platforms such as LiNbO₃ and InP. Silicon-on-insulator (SOI)platform, which can be used to make optical waveguide, has appeared asthe emerging technology for optoelectronics devices including MZMmodulators since SOI fabrication infrastructure is compatible with CMOStechnology and is suitable for photonic integration; however, the mostpromising technology for SOI based optical modulation, which usescarrier depletion through doped P-N junction, suffers high optical lossand high Vpi, where Vpi is defined as the voltage required to generatePi phase shift on MZM arms. High Vpi requires high driver voltage andthus high power consumption for modulator drivers, which limit to theirapplications where low power consumptions are required. In additional,high speed modulators are required to meet the ever-increasing bandwidthrequirements for today's communication and data center interconnectapplications.

An MZM modulator is formed by splitting input optical waveguide into twooptical waveguide arms that operate as phase shifters due toelectro-optic coupling, which are then combined to form a combinedinterference signal based on the Mach-Zehnder interferometer structure.By modulating phases on phase shifters, the optical phase and amplitudemodulations can be achieved. The most promising method for silicon baseoptical modulators is to use carrier depletion which consists of a P-Njunction inside an optical waveguide. Under the reverse bias condition,the P-N junction depletes carrier and causes a change in refractiveindex and the phase change as light propagates through the waveguidewith the refractive index change. In traveling wave structure basedmodulators, a phase shifter has overlapped RF and optical waveguides,which can realize electrical-to-optical (E-O) conversion, characterizedas phase change (degree) on optical wave propagated along the phaseshifter per unit voltage applied to phase shifter. This structure isattractive for high speed linear modulators.

SUMMARY OF THE INVENTION

In a first aspect, the invention pertains to an optical modulatorcomprising a semiconductor-based optical waveguide and a pair of RFwaveguides, wherein the optical waveguide and the RF waveguide areconfigured with coupling regions to provide an RF electromagnetic fieldwithin the optical waveguide and with one or more compensation sectionswith lengths of either optical waveguide or RF waveguide that havesubstantially reduced or eliminated electro-optical coupling. Generally,the RF waveguides form a continuous waveguide structure through the oneor more compensation sections.

In a further aspect, the invention pertains to an optical modulatorcomprising a semiconductor-based optical waveguide and a RF waveguideconfigured to form an coupling region over which electro-opticalcoupling occurs to modulate an optical signal within thesemiconductor-based optical waveguide, wherein the semiconductor-basedoptical waveguide comprises a p-n junction formed according tocorresponding doping of the semiconductor along a cross section throughthe optical waveguide perpendicular to a light propagation direction, inwhich the doping varies at one or more compensation sections along thesemiconductor-based optical waveguide to reduce accumulated phasedifference between an optical transmission in the semiconductor-basedoptical waveguide and an RF signal in the RF waveguide.

In another aspect, the invention pertains to a method for modulating anoptical signal comprising the steps of propagating optical laser lightdown a semiconductor optical waveguide, and propagating RF signal alonga pair of RF waveguides. Generally, the semiconductor optical waveguideand the RF waveguide are configured in a traveling wave modulatorstructure to provide electro-optical coupling, and the traveling wavemodulator structure comprise one or more compensation sections at whichthe relative phase of the propagating optical light and the propagatingRF signal are corrected for a propagating speed differential in whichthe optical signal is modulated by a single RF signal.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic top view of a Mach-Zehnder modulator with atraveling wave structure having RF waveguides interfacing with therespective arms of a Mach-Zehnder interferometer.

FIG. 2 is a plot of relative phase of a propagating signal in a RFwaveguide and an optical signal in an optical waveguide in which withoutphase correction the RF waveguide velocity is greater than the opticalwaveguide velocity with one curve showing the phase mismatch withoutphase correction and a second curve showing the effects of phasecorrection as described herein.

FIG. 3 is a plot of relative phase of a propagating signal in a RFwaveguide and an optical signal in an optical waveguide in which withoutphase correction the RF waveguide velocity is less than the opticalwaveguide velocity with one curve showing the phase mismatch withoutphase correction and a second curve showing the effects of phasecorrection as described herein.

FIG. 4 is a top view of an optical waveguide with three compensationsections having altered semiconductor dopant levels to compensate forthe RF and optical relative phase shift to reduce the phase shift value,in which the RF waveguide is separated to allow separate viewing of theoptical waveguide.

FIG. 5 is the assembled view of the structure of FIG. 4 in which the RFwaveguide is mounted on top of the optical waveguide.

FIG. 6 is a top schematic view of a semiconductor optical waveguidecoupled to an RF waveguide in which compensation sections have extendedportions of optical waveguides extending away from the RF waveguides.

FIG. 7 is a top schematic view of a semiconductor optical waveguidecoupled to an RF waveguide in which compensation sections have extendedportions of RF waveguides extending away from the optical waveguides.

FIG. 8 is a top schematic view of a semiconductor optical waveguidecoupled to an RF waveguide in which a first type of compensationsections have altered semiconductor doping levels and a second type ofcompensation sections have extended portions of optical waveguidesextending away from the RF waveguides.

FIG. 9 is a top schematic view of a semiconductor optical waveguidecoupled to an RF waveguide in which a first type of compensationsections have altered semiconductor doping levels and a second type ofcompensation sections have extended portions of RF waveguides extendingaway from the optical waveguides.

FIG. 10 is a plot of phase differences for a particular model describedbelow.

FIG. 11 is a plot of electro-optical S21 transmission properties as afunction of frequency for three model systems with phase compensationand three corresponding model systems without phase compensation.

FIG. 12 is a top view of a traveling wave Mach-Zehnder modulator with arepresentative compensation section on each interferometer arm toprovide a context for some representative specific waveguide structuresin subsequent figures.

FIG. 13 is a sectional view taken along line A-A of FIG. 12 depicting asilicon-on-insulator (SOI) based optical waveguide with an n-p junctionalong a rib providing for optical propagation along the rib with highlydoped semiconductor wings providing for an interface with RF waveguides.

FIG. 14 is a sectional view taken along line B-B of FIG. 12 depicting afirst type of compensation section with an altered semiconductor dopinglevel.

FIG. 15 is a sectional view taken along line B-B of FIG. 12 depicting asecond type of compensation section in which the RF waveguide extendsaway from the continuing optical waveguide.

FIG. 16 is a fragmentary top view of the compensation section of FIG. 15showing the RF waveguides extending away from optical waveguides.

FIG. 17 is a sectional view taken along line B-B of FIG. 12 depicting athird type of compensation section in which the optical waveguideextends away from the continuing RF waveguide.

FIG. 18 is a fragmentary top view of the compensation section of FIG. 16showing the optical waveguides extending away from RF waveguides.

FIG. 19 is a sectional view of a configuration of a traveling wave MZMwith dual p-n optical waveguides in which an RF waveguide interfaceswith the pair of optical waveguides to perform the electro-opticalcoupling to modulate the optical signal in which semiconductor doping isconfigured to provide an interface of the RF waveguides with n++ dopedwings extending from the ridge optical waveguides.

FIG. 20 is a sectional view of a configuration of a traveling wave MZMwith dual p-n optical waveguides in which an RF waveguide interfaceswith the pair of optical waveguides to perform the electro-opticalcoupling to modulate the optical signal in which semiconductor doping isconfigured to provide an interface of the RF waveguides with p++ dopedwings extending from the ridge optical waveguides.

FIG. 21 has an upper image that is a top view of a traveling wavemodulator with compensation sections to provide improved phase matchingand a lower image that is a sectional view depicting a traveling waveMZM structure with dual p-n optical waveguides interfacing with RFwaveguides.

FIG. 22 has a central image that is a top view of a traveling wavemodulator with two distinct segments having reversed dopant symmetry, alower image that is a sectional view depicting a traveling wave MZMstructure with dual p-n optical waveguides with a first dopant symmetryinterfacing with RF waveguides, and an upper image that is a sectionalview depicting a traveling wave MZM structure with dual p-n opticalwaveguides with a second dopant symmetry reversed from the first dopantsymmetry interfacing with the RF waveguides.

FIG. 23 has a central image that is a top view of a traveling wavemodulator with two distinct segments having reversed dopant symmetrysimilar to FIG. 22 but with compensation sections with modified dopantlevels similar to FIG. 20 to provide for improved phase matching, alower image that is a sectional view depicting a traveling wave MZMstructure with dual p-n optical waveguides with a first dopant symmetryinterfacing with RF waveguides, and an upper image that is a sectionalview depicting a traveling wave MZM structure with dual p-n opticalwaveguides with a second dopant symmetry reversed from the first dopantsymmetry interfacing with the RF waveguides.

FIG. 24 has a central image that is a top view of a traveling wavemodulator with alternating distinct segments having reversed dopantsymmetry similar to FIG. 22 in which the segments with a particulardopant symmetry have a compensation section with modified dopant levelssimilar to FIG. 20 to provide for improved phase matching, a lower imagethat is a sectional view depicting a traveling wave MZM structure withdual p-n optical waveguides with a first dopant symmetry interfacingwith RF waveguides, and an upper image that is a sectional viewdepicting a traveling wave MZM structure with dual p-n opticalwaveguides with a second dopant symmetry reversed from the first dopantsymmetry interfacing with the RF waveguides.

DETAILED DESCRIPTION OF THE INVENTION

RF driven optical modulator structures are described that can compensatefor phase misalignment between an RF signal and an optical signal withina traveling wave electro-optical coupling structure with a Mach-Zehndermodulator (MZM) design. The modifications to provide phase compensationare particularly applicable to semiconductor based optical waveguides,especially silicon-based optical waveguides. As used herein,silicon-based refers to elemental silicon materials that can be dopedand does not refer to silicon dioxide based glass waveguides. To adjustthe relative phases of the optical propagation and RF propagationthrough the coupled waveguides of the traveling wave structure, in someembodiments, either the optical waveguide or the RF waveguide in acompensation section can be looped out of a coupling configuration tophase shift the propagations relative to each other for better phasealignment upon rejoining of the two signals. In additional oralternative embodiments, the dopant levels of the optical waveguide canbe altered in a compensation section to change the relative propagationspeeds of the RF signal and optical signal through the respective twowaveguides to correct for phase shifting of the signals. The resultingmodulator can be suitable for high speed MZM modulators.

In silicon-based optical modulators (e.g., silicon-on-insulator (SOI))or other semiconductor based optical modulators, the optical waveguideis designed with a p-n junction at a phase shifter, i.e.,electro-optical coupled sections of the modulator, with various dopingfor carrier depletions, while the RF waveguide is overlapped withoptical waveguide in phase shifter with various RF coplanar waveguide(CPW) configurations such as SG, SS, GSG, GSSG, etc., where S refers toRF signals with voltages relative to ground and G refers to ground, toachieve electro-optical modulations. Optical waveguide loss can bereduced by refining the fabrication process with optical-propertyoptimizations such as improving roughness of side wall in opticalwaveguides and low doping. Low loss optical waveguides can enable longtravel optical waveguide for modulators, which has potential to achievehigh overall electro-optical (E-O) conversion efficiency and thus lowVpi which is determined by the E-O conversion efficiency (per unitlength) and overlapped length of RF and optical waveguides. However,long overlapped RF and optical waveguides generally have a phasemismatch between RF and optical waves propagated along waveguides,especially at high frequency, which can reduce the overall E-Oconversion efficiency and E-O response bandwidth.

To achieve improved phase-matched RF and optical wave propagation, onepossible method is to introduce a physical distributed capacitance asimplemented in conventional InP travel waveguide modulators as shown ina hybrid format in Chen et al., “25 Gb/s hybrid silicon switch using acapacitively loaded traveling wave electrode,” Optics Express Vol.18(2), January 2010, pp 1070-1075, incorporated herein by reference.However, SOI waveguide has small physical sizes typical less than 1micron, with typical waveguide height 0.2-0.3 microns and width 0.4-0.5microns, and an RF waveguide needs an accurate design to achieve thedesired overlap between RF field mode and doping (p-doping) area inoptical waveguide for high efficiency E-O conversion. Thus, it isgenerally impractical to implement extra physical structures such asdistributed capacitance to adjust RF waveguide or optical waveguidevelocity. Another method to improve phase matching is to change thedoping since the doping has major impact on the RF velocity through thechange in equivalent capacitor in P-N junction. However, dopingconcentration, such as low doping, may be selected for performanceimprovement, such as low optical loss.

To achieve high E-O conversion efficiency (per unit length) in carrierdepletion SOI modulator, high doping P-N junction has been widely used;however, high doping will also suffer high optical loss (per unitlength). Thus, a relative short length of optical/RF waveguide isconsidered to compromise optical loss and E-O conversion or Vpi.

To reduce driver swing voltage requirement in SOI base MZM modulator, acommon method is to use distributed RF/optical waveguides with adistributed drivers as shown in U.S. Pat. No. 7,317,846 to Keil(hereinafter the '846 patent), entitled “Propagation Delay Variation fora Distributed Optical Modulator Driver,” incorporated herein byreference. This method for reducing driver swing voltage requirementsgenerally suffers with respect to accurate control on the phase delaybetween distributed drivers. Therefore, this method is not consideredsuitable to high performance applications such as pulse amplitudemodulation (PAM) and M-ary quadrature amplitude modulation (M-QAM)modulator, where linear and phase control is precisely required. Adriver for PAM modulation is described generally in published U.S.patent application 2017/0346570 to Teranishi, entitled “Method ofControlling Optical Transmitter Operable for Pulse-Amplitude ModulationSignal,” incorporated herein by reference. A driver for QAM modulationis described in published U.S. patent application 2017/0134096 to Zhenget al., entitled “Optical N-Level Quadrature Amplitude Modulation (NQAM)Generation Based on Phase Modulator,” incorporated herein by reference.A similar structure as in the '846 patent is also described in publishedU.S. patent application 2017/0285437 to Doerr et al., entitled “SiliconModulators and Related Apparatus and Methods,” incorporated herein byreference.

Herein, innovative structures are proposed to address the problemsoutlined above to achieve high speed and high efficiency linear MZMmodulator. A basic MZM structure is shown in FIG. 1. Mach-Zehndermodulator element 100 comprises an input optical waveguide 102 that isconnected to optical splitter 104 that connects to first opticalwaveguide arm 106 and second optical waveguide arm 108. Each opticalwaveguide arm is coupled to one or more RF waveguides, respectively,112, 114. RF waveguides 112, 114 are connected to an RF generator 110.The interface between optical waveguide arms 106, 108 and RF waveguides112, 114 form respective coupling regions 116, 118. Optical waveguidearms 106, 108 join at optical coupler 120, which is then connected tooutput waveguide 122. The structures described herein to provide forimproved optical phase and RF phase matching (compensation sections)have intermittent regions of phase matching that may not have high orany electro-optical coupling, but the phase matching nevertheless isdesigned to improve the overall electro-optical coupling due to theimproved phase matching.

Referring to FIG. 2, a schematic plot is shown of the phase mismatchbetween the optical waveguide and the RF waveguide as a function ofdistance along the waveguide for an embodiment with an RF waveguidevelocity greater than optical waveguide velocity. With no phasecorrection, the phase difference grows with distance along thewaveguide, which is contrasted with the phase difference withintermittent correction that keeps the phase difference nearer to thezero-phase difference line and within selected boundaries. Phasedifferences, or ‘walkoff’, of greater than about ±30° will start tonoticeably reduce the modulation efficiency, effectively leading to anincrease in Vpi. Phase walkoff greater than ±90° will actually reversethe modulation efficiency and cannot be overcome even with substantialincrease of Vpi. Depending on, and in consideration of, the collateral‘costs’ of the intermittent corrections, one would typically attempt tokeep the walkoff from exceeding about ±60°, such thatmodulation-efficiency drops would not drop below about 50%.

Referring to FIG. 3, a schematic plot is shown of the phase mismatchbetween the optical waveguide and the RF waveguide as a function ofdistance along the waveguide for an embodiment with an optical waveguidevelocity greater than RF waveguide velocity. Again, with no phasecorrection, the phase difference magnitude grows in a negative directionrelative to a zero phase shift with distance along the waveguide, whichis contrasted with the phase difference with intermittent correctionthat keeps the phase difference nearer to the zero-phase difference lineand within selected boundaries. The phase correction shown in FIG. 3 isin the opposite direction from the phase correction shown in FIG. 2.

As described herein, phase correcting structures and correspondingmethods are designed to achieve better phase-matched RF propagation andoptical wave propagation, where the phase is intermittently re-alignedthrough the (phase) compensation sections in segmented structures. Afirst approach involves addition of compensation sections with altereddoping including lower doping (up to no doping) or higher doping,dependent on the phase sign (delay or advance) between RF and opticalpropagation waves. This embodiment of the coupled waveguides is shownschematically in FIGS. 4 (separated view) and 5 (top view). Referring toFIGS. 4 and 5, optical waveguide 130 comprises compensation sections132, 134, 136 in which the dopant levels are significantly altered fromthe remaining sections of waveguide. RF waveguide 138 interfaces withoptical waveguide 130 to provide electro-optical coupling. Theembodiments of the optical waveguides with lower doping concentration orno doping in compensation sections can reduce the equivalent capacitancein p-n junction which increases RF wave velocity, while the higherdoping can increase equivalent capacitance in p-n junction which slowsdown RF wave velocity. As the doping has much less impact on opticalwave velocity, by proper design in length and doping in the compensationsections, we can achieve the improved phase-matched RF and optical wavepropagations.

While FIGS. 4 and 5 depict three compensation sections, the waveguidescan alternatively have 1, 2, 4, 5, 6, 7, 8, 9, 10, or more than 10compensation sections, which can be selected to achieve desired phasematchings balanced against processing convenience. As described furtherbelow, a cross section of the semiconductor waveguides can be patternedwith various doped sections and a p-n junction generally located alongthe waveguide portion of the semiconductor. For silicon-basedwaveguides, the RF electrodes can be attached to highly doped portionsof the structure adjacent to the doped regions connecting to the p-njunction of the waveguide, with some representative specific structurespresented below. The compensation sections generally involvemodification of dopant levels in the semiconductor sections contactingthe RF waveguides, although the dopant level modifications can extend toother sections of the semiconductor structure. The silicon semiconductorcontacting the RF electrode away from the compensation sections can havea dopant concentration generally of at least about 1×10¹⁸/cm³ and insome embodiments at least about 1×10¹⁹/cm³, up to potentially very highdopant levels. Suitable dopants for silicon, i.e., elemental silicon(Si), are well known in the art, such as phosphorous (n-dopant) andboron (p-dopant). As noted above, at compensation sections, a reduceddopant concentration can be essentially zero, i.e., backgroundcontaminant levels, or at some intermediate value between zero and theselected dopant concentrations away from the compensation sections, andan increased dopant concentration can be at least about 5% greater, inother embodiments at least about 10% greater, and in further embodimentsat least about 30% greater dopant concentration than at correspondingportions of the waveguide away from the compensation sections. A personof ordinary skill in the art will recognize that additional ranges ofnumbers of compensation sections and dopant concentrations within theexplicit ranges above are contemplated and are within the presentdisclosure.

A second approach to providing phase correction involves adding extraoptical waveguide length or adding extra RF waveguide length, dependenton the phase sign (i.e., phase delay or advance) between RF and opticalpropagation waves. An embodiment of the coupled waveguides withcompensation sections having extra optical waveguide length is shownschematically in FIG. 6. Optical waveguide 150 has compensation sections152, 154, 156 each having an extra length of optical waveguide. RFwaveguide 158 couples to optical waveguide 150 away from compensationsections 152, 154, 156, where the electro-optical coupling issignificantly reduced or eliminated. An embodiment of the coupledwaveguides with compensation sections having extra RF waveguide lengthis shown schematically in FIG. 7. Referring to FIG. 7, RF waveguide 160has compensation sections 162, 164, 166 each having an extra length ofRF waveguide, and optical waveguide 168 couples to RF waveguide 160primarily or exclusively away from compensation sections 162, 164, 166.FIGS. 6 and 7 depict structures with three compensation sections eachwith extended waveguides, and in other embodiments the structures canhave 1, 2, 4, 5, 6, 7, 8, 9, 10, or more than 10 compensation sectionseach with extended portions of either optical waveguide or RF waveguidethat extends away from electro-optically coupled portions of thestructure. Each extended waveguide portion generally has a length thatis at least about 1%, in further embodiments at least about 5%, and inother embodiments at least about 15% of the total waveguide length alongthe modulation section. A person or ordinary skill in the art willrecognize that additional ranges of numbers of compensation sections andlength of waveguides in compensation sections within the explicit rangesabove are contemplated and are within the present disclosure.

As the second approach for phase correction uses the compensationsections with extra length of RF waveguide or optical waveguide that donot have overlapping RF waveguide and optical waveguide, there issignificantly reduced or no electro-optical conversions in thecompensation sections. In addition, optical loss or RF loss in thesecompensation sections can introduce extra optical or RF loss after eachcompensation section, which also can reduce overall electro-opticalconversions. Different from the second approach, the first approach withthe compensation sections having lower doping or higher doping allows RFand optical waveguide to be overlapped in the compensation sections, theoverall electro-optical conversion efficiency can be improved. However,the change in RF velocity due to the change in the doping is limited. Athird approach can provide for high efficiency overall electro-opticalconversions by combining the first approach and the second approach.Through appropriate design of the combined compensation sections in thephase shifter, an increased electro-optical conversion efficiency can beachieved for high speed linear MZM modulators. Referring to FIG. 8,optical waveguide 170 has dopant-based compensation sections 172, 174,176, 178, where the dopant levels are reduced (up to no dopant) orincreased relative to the remaining sections of optical waveguide, andextra length based compensation sections 180, 182, 184. RF waveguide 186is configured to provide electro-optical coupling with optical waveguide170 except for reduced or eliminated electro-optical coupling alongextra length based compensation sections 180, 182, 184. Referring toFIG. 9, optical waveguide 200 has dopant-based compensation sections202, 204, 206, 208, and RF waveguide 210 has extra length-basedcompensation sections 212, 214, 216. RF waveguide 210 is configured toprovide electro-optical coupling with optical waveguide 200 except forreduced or eliminated coupling at extra length-based compensationsections 212, 214, 216.

As shown in FIGS. 8 and 9, the compensation sections based on dopantconcentration changes generally are at different physical locations thancompensation sections based on extended waveguide lengths. As notedabove, the number of each type of compensation sections can be selectedwithin reasonable ranges. While there is some symmetry with thealternating style of FIGS. 8 and 9, there is no need for such a design,so any reasonable order and positioning along the length of thewaveguides can be used for the different types of compensation sections.The dopant levels and lengths for waveguide extensions are describedabove in the context of FIGS. 4-7, and these parameters are equallyapplicable as if written here for the embodiments of FIGS. 8 and 9,which involve a combination of these features.

While FIGS. 4-9 provide informative depictions of various embodiments ofthe improved structures herein, more specific details are provided belowfor some specific embodiments of the various waveguides. With respect toevaluation of the phase shifts, the accumulated phase difference betweenRF and optical waveguide can be expressed by following equation:

$\begin{matrix}{\varphi = {{\int{\frac{2\pi\; f_{m}}{v_{rf}\left( l_{rf} \right)}{dl}_{rf}}} - {\int{\frac{2\pi\; f_{m}}{v_{opt}\left( l_{opt} \right)}{dl}_{opt}}}}} & (1)\end{matrix}$Where, φ is accumulated phase difference between RF and opticalwaveguides, f_(m) is modulation frequency, υ_(rf) is travel wavevelocity of RF waveguide, υ_(opt) is travel wave velocity of opticalwaveguide, l_(rf) and l_(opt) are RF and optical waveguide lengths,respectively. In some embodiments, the design goal is to keep theaccumulated phase (φ) within desired boundary values along the RF andoptical travel waveguides by periodic compensation to achieve highefficiency for high speed linear modulations. The decrease inaccumulated phase difference generated by the embodiments in FIGS. 4-9can be understood in terms of the changes introduced in equation (1).

In general, the waveguides comprise multiple compensation sections inalternating configurations with other sections that provide theelectro-optic coupling. In some embodiments, the alternatingcompensation sections can be periodic, i.e., alternating isapproximately equally spaced increments along the length of thewaveguide. With respect to periodic compensation sections, the periodiccompensations in the segmented structures may potentially generate thedistributed reflections along RF or optical waveguides between segments,depending on design requirements, which may form the resonantstructures. To avoid the impact of such resonant structures forapplications, the segment length period is required to be smaller tomove resonant frequencies above operating frequency range as thefollowing formulae:fop<fr=c/(2*n*Lseg)  (2)Where fop is operating frequency of MZM applications, fr is resonantfrequency due to distributed reflection from segmented structures, c isoptical velocity, n is effective index for optical or RF waveguide whichis defined as the ratio of optical speed (c) to optical or RF wavevelocity, and Lseg is the period of segment length.

For an effective index of refraction of 3.9 for a silicon-based opticalwaveguide, the length of the period can be equal to less than 500microns to have the resonance above 75 GHz which is sufficient for 64GB/s applications, or equal to less than 250 microns to have theresonance above 150 GHz for 120 GB/s applications. In an example designof a MZM, effective optical index for optical waveguide is 3.9 while theeffective RF index for doped RF waveguide is 3.3. This refractive indexmismatch can cause a phase mismatch and low band width. In this designexample, 3 dB electro-optical band width (EO BW) can be improved from 28GHz to 36G for 10 mm long phase shifter and from 13 GHz to 18 GHz for 4mm long phase shifter with the segmented phase compensation as describedin this disclosure. The period of the compensation segment length of 500microns is used for the estimates. For this model, the phase differencewith and without compensation is shown in FIG. 10. FIG. 11 shows theelectro-optical S21 transmission response for three modulator lengthswith and without compensation as a function of transmission frequency.For a particular error tolerance, the compensated signals providesdesirable bandwidths to higher frequencies. The compensation can beeither adding high doping sections or adding extra RF waveguides orcombination of both to slow down RF propagation for phase match opticaland RF wave propagation as proposed in this disclosure.

While the compensation segments may or may not be periodic, the distancescales above provide useful reference points. In general, the lengths ofthe optical waveguide and coupled RF waveguides can be from about 1 mmto about 30 mm and in further embodiments from about 2 mm to 25 mm, witha portion of the length interrupted by the compensation segments. Insome embodiments, the compensation segments can have lengths from about5 microns to about 100 microns and in further embodiments from about 7.5microns to about 75 microns. In some embodiments, the edge to edgespacing between adjacent compensation sections can be from about 35microns to about 2000 microns and in further embodiments from about 50microns to about 1500 microns, and for non-periodic embodiments, thesevalues can be considered averages. A person of ordinary skill in the artwill recognize that additional ranges within or of similar order tothese explicit ranges are contemplated and are within the presentdisclosure.

While the discussion herein focuses on silicon-based optical waveguides,the principles are generally applicable to other modulator structureswith semiconductor optical waveguides, such as indium phosphate (InP) orlithium niobate (LiNbO₃) waveguides. However, for silicon-basedmodulators, the difficulty in identifying alternative solutions to thephase delay issue underscores the significance of the present structuresfor silicon-based modulators. Indium phosphide modulator structures aredescribed, for example, in copending U.S. patent application Ser. No.15/462,099 to Chen et al., “High Frequency Optical Modulator WithLaterally Displaced Conduction Plane Relative to Modulating Electrodes,”incorporated herein by reference. Lithium niobate based modulators aredescribed for example in published U.S. patent application 2017/0052424to Iwatsuka et al., entitled “Optical Waveguide Element and OpticalModulator Using the Same,” incorporated herein by reference.

The structures with phase-matched optical and RF wave propagation can beapplied to different MZM structures. Representative examples arepresented below of traveling wave MZM structures with two RF waveguidesfor two p-n waveguides, and of traveling wave MZM structures with singleRF waveguide for dual p-n waveguides. The structures with phase-matchedoptical and RF wave propagation can be combined with other waveguidesections in proper way for the compensation of imbalance of such as lossand modulation efficiency based on design considerations known in theart.

A traveling wave Mach-Zehnder modulator (TW-MZM) structure 250 is shownin FIG. 12. TW-MZM structure 250 comprises input optical waveguide 252,splitter 254, first optical waveguide arm 256, first RF waveguidecomponent 258, first compensation section 260, second optical waveguidearm 262, second RF waveguide component 264, second compensation section266, optical combiner 268, output optical waveguide 270 and RF driver272. Various optical splitters/combiners are known in the art, andsimple division/combining of the waveguide can be acceptable if theoptical loss is within design parameters. Reduced loss designs aredescribed, for example, in copending U.S. patent application Ser. No.15/490,420 to Ticknor et al., entitled “Planar Lightwave CircuitSplitter/Mixer,” incorporated herein by reference. For single MZM TWwith dual p-n waveguides, the long waveguide can increase the imbalanceof insertion loss and modulation efficiency due to p-n dopingmisalignment which causes one p-n with overlap and the other p-n withgap although the phase-match can be achieved. The structure withphase-matched sections proposed in this disclosure allow combining thesections for the compensation of imbalance of loss and modulationefficiency between two arms of MZM due to the p-n doping misalignment toachieve high extinction ratio.

RF drivers are discussed further above. RF driver 272 can be connectedappropriately to RF waveguide components 258, 264 depending on theconfiguration of the RF electrodes. FIG. 13 depicts a structure with anRF electrode pair positioned around a single optical waveguide, andanother comparable RF electrode pair driven with the same or differentRF generator would be positioned around the optical waveguide on theother corresponding optical waveguide arm. FIGS. 19 and 20 depict an RFelectrode pair positioned around a pair of optical waveguides. Theseembodiments are described further below.

FIG. 12 shows only a single compensation section for convenience sincethe purpose is to provide a context for description of some morespecific representative embodiments of the compensation sections. Asnoted above, an MZM structure can have different numbers of compensationsections along the traveling wave coupled waveguides to achieve desiredphase matching, and the additional compensation sections generally canhave analogous structures as each other. The following figures depictrepresentative embodiments of traveling wave structures and compensationsections.

A sectional view of a traveling wave RF waveguide with a single p-njunction optical waveguide is shown in FIG. 13 taken along line A-A ofFIG. 12. The silicon-on-insulator (SOI) overall structure can have asilicon substrate 300 supporting the structure. Insulation layer 302 canbe placed over a smooth surface of silicon substrate 300. Insulationlayer 302 can comprise a non-electrically conducting ceramic, such asSiO₂ (silica) or sapphire (alumina) Al₂O₃ or other appropriate material.The optical waveguide is then formed on insulating layer 302. Theoptical waveguide in FIG. 13 is optical waveguide ridge 304 with a p-njunction running along the ridge with a vertical interface in theorientation of the figure, comprising p-doped domain 306 and n-dopeddomain 308. In the embodiment of FIG. 13, higher doped wings extend fromthe edges of the ridge with a p++ domain 310 extending from p-dopeddomain 306 and n++ domain 312 extending from n-doped domain 308. RFwaveguide electrodes 314, 316 interface, respectively, with p++ domain310 and n++ domain 312. A polymer, silica or other cladding material 318can be used to cover exposed portions of the optical waveguide, althoughair may suffice as a cladding.

The formation of doped silicon optical waveguide components can beformed using chemical vapor deposition and photolithography. The RFwaveguides can be formed from metal or other electrical conductivematerial. Metal can be deposited, for example, using physical vapordeposition, such as sputtering, or other suitable method, and metal canbe patterned also using photolithography or laser ablation etching.

FIGS. 14-18 depict cross sections of compensation section 266 takenalong line B-B of FIG. 12 for three different embodiments. Referring toFIG. 14, components of the optical waveguides have modified dopantlevels. Thus, wing waveguide components 330 and 332 have differentdopant levels relative, respectively, to p++ domain 310 and n++ domain312 of FIG. 13. Corresponding waveguide ridge 334 components 336, 338may or may not have different dopant levels relative to correspondingridge waveguide components p-doped domain 306 and n-doped domain 308 ofFIG. 13. As described above, the change in dopant levels can be adecrease (optionally down to 0) or an increase.

Referring to FIGS. 15 and 16, in this embodiment, compensation section266 (FIG. 12) has RF waveguide extensions. FIG. 15 has a sectional viewalong line B-B of FIG. 12 in which the RF waveguide is turned out of theview, and FIG. 16 has a fragmentary top view depicting the extension ofthe RF waveguide through curvature of the RF waveguide away from theoptical waveguides. The optical waveguide components shown in FIG. 15are essentially as shown in FIG. 13 except for the absence of the RFwaveguide components. Referring to FIG. 16, RF waveguide electrode 314overlapping with the corresponding optical waveguides connect with RFwaveguide extension 350 with a waveguide path that is curved away fromthe optical waveguide with optical waveguide ridge 304, (waveguide wing)p++ domain 310, and (waveguide wing) n++ domain 312. Similarly, RFwaveguide electrode 316 overlapping with corresponding opticalwaveguides connect with RF extension 352 with a waveguide path that iscurved away from the optical waveguide. For RF extensions 350, 352,there is considerable design flexibility in the shape of the componentswith suitable patterning available generally, and the lengths can beselected to achieve desired phase matching as described above, which theschematic view in FIG. 16 is selected to give the idea of the structurewithout suggesting any particular shape or length. The lengths of the Fextensions may or may not be the same.

Referring to FIGS. 17 and 18, in this embodiment, compensation section266 (FIG. 12) has optical waveguide extensions. FIG. 17 has a sectionalview along line B-B of FIG. 12 in which the optical waveguide is turnedout of the view, and FIG. 18 has a fragmentary top view depicting theextension of the optical waveguide through curvature of the opticalwaveguide away from the RF waveguides. The RF waveguide components shownin FIG. 17 are essentially as shown in FIG. 13 except for the absence ofthe optical waveguide components. Referring to FIG. 18, opticalwaveguide ridge 304 component of the optical waveguide connects withridge waveguide extension 360, p++ domain 310 component of the opticalwaveguide connects with p++ waveguide extension 362, and n++ domain 312of the optical waveguide connects with n++ waveguide extension 364. Thedesign of optical waveguide extensions can provide proper attention topotential optical loss resulting from waveguide curves, although therelatively high index of refraction of silicon allows for more curvaturewith acceptable loss than many other optical materials. Also, the lengthof the optical waveguide extensions can be selected to achieve a desiredphase matching, and the depiction of the waveguide extension in FIG. 18is directed to indicating the general idea of the optical waveguideextension and is not intended to depict any particular relative lengthof the optical waveguide extension. Other p-n diode structures can beeffectively used to form the optical waveguide, such as a silicon-basedp-n junction optical waveguides with both horizontal and vertical p-ninterfaces suitable for phase correction as described herein aredescribed in U.S. Pat. No. 9,541,775 to Ayazi et al., entitled “Methodand System for a Low-Voltage Integrated Silicon High-Speed Modulator,”and a horizontal p-n junction as described in U.S. Pat. No. 8,320,720 toWebster et al., entitled “Advanced Modulation Formats for Silicon-BasedOptical Modulators,” both of which are incorporated herein by reference.

FIGS. 19 and 20 show embodiments of a single traveling wave RFelectrodes interfaced with a pair of p-n optical waveguides. Thesetraveling wave electro-optical coupling structures can be considered inthe context of FIG. 12, and analogous compensation sectionscorresponding to FIGS. 14-18 (dopant adjustment (FIG. 14), extended RFwaveguides (FIGS. 15, 16) and extended optical waveguides (FIGS. 17,18)) can be used to phase correct the propagating signals through the RFwaveguides and the optical waveguides of FIGS. 19 and 20, as well as forthe structures in FIGS. 19-22 discussed in detail below.

Referring to FIG. 19, patterned doped silicon over insulating layer 302on silicon substrate 300 forms two p-n interfaced ridge opticalwaveguides 400, 402 respectively comprise n-doped region 404, p-dopedregion 406, n-doped region 408 and p-doped region 410. A p++ region 412connects p-doped region 406 and p-doped region 410 along the center ofthe doped silicon structure. A n++ wing 414 extends from n-doped region404, and n++ wing 416 extends from n-doped region 408. RF waveguidecomponents 418, 420 interface respectively with n++ wing 414 and n++wing 416. Cladding 422 covers exposed portions of the doped silicon.

Referring to FIG. 20, patterned doped silicon over insulating layer 302on silicon substrate 300 forms two p-n interfaced ridge opticalwaveguides 430, 432 respectively with reversed dopant configurationsrelative to the embodiment in FIG. 19. Ridge optical waveguide 430comprises n-doped region 434 and p-doped region 436, and ridge opticalwaveguide 432 comprises n-doped region 438 and p-doped region 440. A n++region 442 connects n-doped region 434 and n-doped region 438 along thecenter of the doped silicon structure. A p++ wing 444 extends fromp-doped region 436, and p++ wing 446 extends from p-doped region 440. RFwaveguide components 448, 450 interface respectively with p++ wing 444and p++ wing 446. Cladding 460 covers exposed portions of the dopedsilicon.

An embodiment of the traveling wave modulator of FIG. 20 withcompensation sections having modified dopant levels is shown in FIG. 21.A top view in the upper portion of FIG. 21 shows traveling wavemodulator 470 with 4 compensation sections 472, 474, 476, 478 dividingsegments 480, 482, 484, 486, 488 with baseline doping levels to achievedesired electro-optical coupling. The sectional view in the lower viewof FIG. 21 shows the doping structure in one of the baseline sections oftraveling wave modulator 470. As shown in the lower view of FIG. 21,optical waveguide ridges 490, 492 has dopant p-n misalignment shown inexaggerated form for view with waveguide ridge 490 having an overlapregion 494 between n-doped region 496 and p-doped region 498 and withwaveguide ridge 492 having a dopant gap 500 between n-doped region 502and p-doped region 504.

To compensate for some of the imbalance of insertion loss and modulatorefficiency due to p-n doping misalignment, whether or not phase matchingis achieved, the alternative dopant structures of FIGS. 19 and 20 can beused for portions of the traveling wave modulator. Referring to a topview in the central image of FIG. 22, traveling wave modulator 520comprises a first section 522 with the dopant structure of FIG. 19 and asecond section 524 with the dopant structure of FIG. 20 along with anyimperfections due to doping misalignment. The sectional view in thelower image of FIG. 22 depicts traveling wave modulator 534 with adopant structure to provide desired electro-optical coupling having adopant structure similar to FIG. 20 but with effects shown for dopantmisalignment in optical waveguide ridge 536 and optical waveguide ridge538. The sectional view in the upper image of FIG. 22 depicts travelingwave modulator 540 with a dopant structure to provide desiredelectro-optical coupling having a dopant structure similar to FIG. 19but with effects shown for dopant misalignment in optical waveguideridge 542 and optical waveguide ridge 544. The use of waveguidestructures with the reversed dopant structures can compensate for someof the imbalance resulting from the dopant misalignment.

The structure in FIG. 22 further allows for the reversal of the phasemodulation to allow for continued accumulation of optical signalmodulation from the electro-optical coupling. Thus, if the phasedifference accumulates to be greater than ±90 degrees, the shift of thephase modulation due to the dopant change allows for continuedaccumulation of the electro-optical phase modulation. If the phasewalk-off reached ±270 degrees, a switch of the dopant type againprovides for continued accumulation of electro-optical phase shift ofthe signal. The process of dopant switching can be continued foradditional walk-off shifts of ±180 degrees. Periodic poling has beenused for lithium niobate based modulators.

Referring to FIG. 23, compensation for dopant misalignment as well asfor the accumulation of phase walk-off beyond ±90 degrees through thereversal of the dopant structure, as shown in FIG. 22 is combined withdopant modification for compensation of phase misalignment as shown inFIG. 21. Referring to a top view of the central image in FIG. 23,traveling wave modulator 550 comprises a first section 552 with thedopant structure of FIG. 19 and a second section 554 with the dopantstructure of FIG. 20 along with any imperfections due to dopingmisalignment. First section 552 comprises compensation sections 556, 558with altered dopant levels for phase matching, and second section 554comprises compensation sections 560, 562 with altered dopant levels forphase matching. The sectional view in the lower image of FIG. 23 depictstraveling wave modulator 564 with a dopant structure to provide desiredelectro-optical coupling having a dopant structure similar to FIG. 20but with effects shown for dopant misalignment in optical waveguideridge 566 and optical waveguide ridge 568. The sectional view in theupper image of FIG. 23 depicts traveling wave modulator 570 with adopant structure to provide desired electro-optical coupling having adopant structure similar to FIG. 19 but with effects shown for dopantmisalignment in optical waveguide ridge 572 and optical waveguide ridge574. In the embodiment of FIG. 23, the use of the dopant structures offirst section 552 and second section 554 can provide imbalancecompensation for some of the issues resulting from dopant misalignmentand the use of compensation sections 556, 558, 560, 562 can provideimproved phase matching. While the number of dopant varying compensationsections in FIG. 23 is shown as two per dopant symmetry, as noted above,the number of compensation sections can be selected as desired from 1 to10 or more.

The organization of first section 552 and second section 554 in FIG. 23can be generalized to provide for more alternation of the dopantsymmetries. Referring to a top view of the central image in FIG. 24,traveling wave modulator 600 comprises segments 602, 604, 606 with afirst dopant symmetry and segments 608, 610, 612 with a reversed dopantsymmetry. Segments 602, 604, 606 respectively comprise compensationsections 620, 622, 624 with altered dopant levels for improved phasematching, and segments 608, 610, 612 respectively comprise compensationsections 626, 628, 630 with altered dopant levels for improved phasematching. While FIG. 24 top view depicts one compensation section persegment, a greater number can be used independently for each segment asdescribed generally above. The sectional view in the lower image of FIG.24 depicts traveling wave modulator 632 with a dopant structure toprovide desired electro-optical coupling having a dopant structuresimilar to FIG. 20 but with effects shown for dopant misalignment inoptical waveguide ridge 634 and optical waveguide ridge 636. Thesectional view in the upper image of FIG. 24 depicts traveling wavemodulator 638 with a dopant structure to provide desired electro-opticalcoupling having a dopant structure similar to FIG. 19 but with effectsshown for dopant misalignment in optical waveguide ridge 640 and opticalwaveguide ridge 642. Based on the disclosure herein, the specificembodiment suggests alternative embodiments using different numbers ofalternating dopant symmetries distinct from the three segments of eachtype of dopant symmetry shown in FIG. 24. In the embodiment of FIG. 24,the use of the dopant structures of first dopant symmetry of segments602, 604, 606 and second dopant symmetry of segments 608, 610, 612 canprovide imbalance compensation for some of the issues resulting fromdopant misalignment, and the use of compensation sections 620, 622, 624,626, 628, 630 can provide improved phase matching.

The embodiments above are intended to be illustrative and not limiting.Additional embodiments are within the claims. In addition, although thepresent invention has been described with reference to particularembodiments, those skilled in the art will recognize that changes can bemade in form and detail without departing from the spirit and scope ofthe invention. Any incorporation by reference of documents above islimited such that no subject matter is incorporated that is contrary tothe explicit disclosure herein. To the extent that specific structures,compositions and/or processes are described herein with components,elements, ingredients or other partitions, it is to be understand thatthe disclosure herein covers the specific embodiments, embodimentscomprising the specific components, elements, ingredients, otherpartitions or combinations thereof as well as embodiments consistingessentially of such specific components, ingredients or other partitionsor combinations thereof that can include additional features that do notchange the fundamental nature of the subject matter, as suggested in thediscussion, unless otherwise specifically indicated.

What is claimed is:
 1. An optical modulator comprising asemiconductor-based optical waveguide and an RF waveguide configured toform a coupling region over which electro-optical coupling occurs tomodulate an optical signal within the semiconductor-based opticalwaveguide, wherein the semiconductor-based optical waveguide comprises ap-n junction formed according to corresponding doping of thesemiconductor along a cross section through the optical waveguideperpendicular to a light propagation direction and wherein the dopingvaries at one or more compensation sections along thesemiconductor-based optical waveguide, relative to other portions of thesemiconductor based optical waveguide, to reduce accumulated phasedifference between an optical transmission in the semiconductor-basedoptical waveguide and an RF signal in the RF waveguide.
 2. The opticalmodulator of claim 1 wherein the one or more compensation sections isthree or more compensation sections.
 3. The optical modulator of claim1, wherein the compensation sections comprise a RF waveguide that turnsaway from the optical waveguide and follows a path that realigns withthe optical waveguide at another end of the compensation section toresume electro-optical coupling away from the compensation section. 4.The optical modulator of claim 1 wherein the compensation sectionscomprise an optical waveguide that turns away from the RF waveguide andfollows a path that realigns with the RF waveguide at another end of thecompensation section to resume electro-optical coupling away from thecompensation section.
 5. The optical modulator of claim 1 furthercomprising dopant compensation section comprising an altered crosssectional dopant profile relative to the semiconductor-based opticalwaveguide away from the compensation section.
 6. The optical modulatorof claim 1 wherein the dopant level of the semiconductor elementinterfacing with a RF electrode in a compensation section has a changeof dopant level or at least about 25% relative to the dopant level ofthe semiconductor element interfacing with a RF electrode away from acompensation section.
 7. The optical modulator of claim 1 wherein thesemiconductor optical waveguide comprises a silicon-based waveguide. 8.The optical modulator of claim 7 wherein the silicon-based opticalwaveguide comprises a p-n dopant interface within a doped silicon ridge.9. The optical modulator of claim 7 comprising a Mach-Zehnder modulatorstructure with an input waveguide, two interferometer arms, an opticalsplitter optically connecting the input waveguide with the twointerferometer arms, wherein one interferometer arm corresponds with thesemiconductor-based optical waveguide.
 10. The optical modulator ofclaim 9 wherein two highly doped silicon wings connect to the dopedsilicon ridge, and wherein RF waveguides interface with each highlydoped silicon wing.
 11. The optical modulator of claim 7 furthercomprising an additional semiconductor based optical waveguidecorresponding with another interferometer arm and having a p-n dopantinterface within a doped silicon ridge, and wherein a highly doped wingextends from each doped silicon ridge extending way from the otherridge, and wherein RF waveguides interface with each highly dopedsilicon wing.